381 research outputs found
Aggregation Operators for Fuzzy Rationality Measures.
Fuzzy rationality measures represent a particular class of aggregation operators. Following the axiomatic approach developed in [1,3,4,5] rationality of fuzzy preferences may be seen as a fuzzy property of fuzzy preferences. Moreover, several rationality measures can be aggregated into a global rationality measure. We will see when and how this can be done. We will also comment upon the feasibility of their use in real life applications. Indeed, some of the rationality measures proposed, though intuitively (and axiomatically) sound, appear to be quite complex from a computational point of view
Degenerate distributions in complex Langevin dynamics: one-dimensional QCD at finite chemical potential
We demonstrate analytically that complex Langevin dynamics can solve the sign
problem in one-dimensional QCD in the thermodynamic limit. In particular, it is
shown that the contributions from the complex and highly oscillating spectral
density of the Dirac operator to the chiral condensate are taken into account
correctly. We find an infinite number of classical fixed points of the Langevin
flow in the thermodynamic limit. The correct solution originates from a
continuum of degenerate distributions in the complexified space.Comment: 20 pages, several eps figures, minor comments added, to appear in
JHE
The QCD sign problem and dynamical simulations of random matrices
At nonzero quark chemical potential dynamical lattice simulations of QCD are
hindered by the sign problem caused by the complex fermion determinant. The
severity of the sign problem can be assessed by the average phase of the
fermion determinant. In an earlier paper we derived a formula for the
microscopic limit of the average phase for general topology using chiral random
matrix theory. In the current paper we present an alternative derivation of the
same quantity, leading to a simpler expression which is also calculable for
finite-sized matrices, away from the microscopic limit. We explicitly prove the
equivalence of the old and new results in the microscopic limit. The results
for finite-sized matrices illustrate the convergence towards the microscopic
limit. We compare the analytical results with dynamical random matrix
simulations, where various reweighting methods are used to circumvent the sign
problem. We discuss the pros and cons of these reweighting methods.Comment: 34 pages, 3 figures, references added, as published in JHE
The running coupling of 8 flavors and 3 colors
We compute the renormalized running coupling of SU(3) gauge theory coupled to
N_f = 8 flavors of massless fundamental Dirac fermions. The recently proposed
finite volume gradient flow scheme is used. The calculations are performed at
several lattice spacings allowing for a controlled continuum extrapolation. The
results for the discrete beta-function show that it is monotonic without any
sign of a fixed point in the range of couplings we cover. As a cross check the
continuum results are compared with the well-known perturbative continuum
beta-function for small values of the renormalized coupling and perfect
agreement is found.Comment: 15 pages, 17 figures, published versio
Associative polynomial functions over bounded distributive lattices
The associativity property, usually defined for binary functions, can be
generalized to functions of a given fixed arity n>=1 as well as to functions of
multiple arities. In this paper, we investigate these two generalizations in
the case of polynomial functions over bounded distributive lattices and present
explicit descriptions of the corresponding associative functions. We also show
that, in this case, both generalizations of associativity are essentially the
same.Comment: Final versio
Ontologies, Mental Disorders and Prototypes
As it emerged from philosophical analyses and cognitive research, most concepts exhibit typicality effects, and resist to the efforts of defining them in terms of necessary and sufficient conditions. This holds also in the case of many medical concepts. This is a problem for the design of computer science ontologies, since knowledge representation formalisms commonly adopted in this field do not allow for the representation of concepts in terms of typical traits. However, the need of representing concepts in terms of typical traits concerns almost every domain of real world knowledge, including medical domains. In particular, in this article we take into account the domain of mental disorders, starting from the DSM-5 descriptions of some specific mental disorders. On this respect, we favor a hybrid approach to the representation of psychiatric concepts, in which ontology oriented formalisms are combined to a geometric representation of knowledge based on conceptual spaces
QCD with Chemical Potential in a Small Hyperspherical Box
To leading order in perturbation theory, we solve QCD, defined on a small
three sphere in the large N and Nf limit, at finite chemical potential and map
out the phase diagram in the (mu,T) plane. The action of QCD is complex in the
presence of a non-zero quark chemical potential which results in the sign
problem for lattice simulations. In the large N theory, which at low
temperatures becomes a conventional unitary matrix model with a complex action,
we find that the dominant contribution to the functional integral comes from
complexified gauge field configurations. For this reason the eigenvalues of the
Polyakov line lie off the unit circle on a contour in the complex plane. We
find at low temperatures that as mu passes one of the quark energy levels there
is a third-order Gross-Witten transition from a confined to a deconfined phase
and back again giving rise to a rich phase structure. We compare a range of
physical observables in the large N theory to those calculated numerically in
the theory with N=3. In the latter case there are no genuine phase transitions
in a finite volume but nevertheless the observables are remarkably similar to
the large N theory.Comment: 44 pages, 18 figures, jhep3 format. Small corrections and
clarifications added in v3. Conclusions cleaned up. Published versio
Is Evolution Algorithmic?
In Darwin’s Dangerous Idea, Daniel Dennett claims that evolution is algorithmic. On Dennett’s analysis, evolutionary processes are trivially algorithmic because he assumes that all natural processes are algorithmic. I will argue that there are more robust ways to understand algorithmic processes that make the claim that evolution is algorithmic empirical and not conceptual. While laws of nature can be seen as compression algorithms of information about the world, it does not follow logically that they are implemented as algorithms by physical processes. For that to be true, the processes have to be part of computational systems. The basic difference between mere simulation and real computing is having proper causal structure. I will show what kind of requirements this poses for natural evolutionary processes if they are to be computational
Additive generators based on generalized arithmetic operators in interval-valued fuzzy and Atanassov's intuitionistic fuzzy set theory
In this paper we investigate additive generators in Atanassov's intuitionistic fuzzy and interval-valued fuzzy set theory. Starting from generalized arithmetic operators satisfying some axioms we define additive generators and we characterize continuous generators which map exact elements to exact elements in terms of generators on the unit interval. We give necessary and sufficient condition under which a generator actually generates a t-nporm and we show that the generated t-norm belongs to particular classes of t-norms depending on the arithmetic operators involved in the defintion of the generator
Lattice QCD at the physical point: Simulation and analysis details
We give details of our precise determination of the light quark masses
m_{ud}=(m_u+m_d)/2 and m_s in 2+1 flavor QCD, with simulated pion masses down
to 120 MeV, at five lattice spacings, and in large volumes. The details concern
the action and algorithm employed, the HMC force with HEX smeared clover
fermions, the choice of the scale setting procedure and of the input masses.
After an overview of the simulation parameters, extensive checks of algorithmic
stability, autocorrelation and (practical) ergodicity are reported. To
corroborate the good scaling properties of our action, explicit tests of the
scaling of hadron masses in N_f=3 QCD are carried out. Details of how we
control finite volume effects through dedicated finite volume scaling runs are
reported. To check consistency with SU(2) Chiral Perturbation Theory the
behavior of M_\pi^2/m_{ud} and F_\pi as a function of m_{ud} is investigated.
Details of how we use the RI/MOM procedure with a separate continuum limit of
the running of the scalar density R_S(\mu,\mu') are given. This procedure is
shown to reproduce the known value of r_0m_s in quenched QCD. Input from
dispersion theory is used to split our value of m_{ud} into separate values of
m_u and m_d. Finally, our procedure to quantify both systematic and statistical
uncertainties is discussed.Comment: 45 page
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